THIS IS A NEW SPECIFICATION H GENERAL CERTIFICATE OF SECONDARY EDUCATION MATHEMATICS A A502/02 Unit B (Higher Tier) *OCE/35068* Candidates answer on the question paper. OCR supplied materials: None Other materials required: Geometrical instruments Tracing paper (optional) Tuesday 9 November 2010 Morning Duration: 1 hour * A 5 0 2 0 2 * INSTRUCTIONS TO CANDIDATES Write your name, centre number and candidate number in the boxes above. Please write clearly and in capital letters. Use black ink. Pencil may be used for graphs and diagrams only. Read each question carefully. Make sure you know what you have to do before starting your answer. Your answers should be supported with appropriate working. Marks may be given for a correct method even if the answer is incorrect. Write your answer to each question in the space provided. Additional paper may be used if necessary but you must clearly show your candidate number, centre number and question number(s). Answer all the questions. Do not write in the bar codes. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. Your Quality of Written Communication is assessed in questions marked with an asterisk (*). The total number of marks for this paper is 60. This document consists of 16 pages. Any blank pages are indicated. WARNING No calculator can be used for this paper [K/600/3701] DC (CW/SW) 35068/3 This paper has been pre modified for carrier language OCR is an exempt Charity Turn over
2 Formulae Sheet: Higher Tier a Area of trapezium = 1 2 (a + b)h h b Volume of prism = (area of cross-section) length crosssection length In any triangle ABC a sin A = b sin B = c Sine rule sin C b C a Cosine rule a 2 = b 2 + c 2 2bc cos A 1 2 Area of triangle = ab sin C A c B Volume of sphere = 4 3 π r 3 Surface area of sphere = 4 π r 2 r Volume of cone = 1 3 π r 2 h Curved surface area of cone = π r l l h r The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a = 0, are given by b ± (b 2 4ac) x = 2a PLEASE DO NOT WRITE ON THIS PAGE
1 (a) Work out. 3 (i) the cube of 5 (a)(i) [1] (ii) 169 (ii) [1] (b) (i) Write as a single power of 5. 5 6 5 4 (b)(i) [1] (ii) Write as a single power of r. r 12 r 3 (ii) [1] (c) Find the value of the following. (i) 16 0 (c)(i) [1] (ii) 27 2 3 (ii) [2] Turn over
2 y 5 4 4 3 F 2 1 5 4 3 2 1 0 1 2 3 4 5 6 7 x 1 2 3 4 5 (a) Rotate shape F 90 anticlockwise about the point (1, 1). Label the image G. [3] (b) Translate shape F using the vector Label the image H. 1 3. [2]
3 A DIY store sells nails in boxes, which are cuboids. 5 2 cm 8 cm 4 cm Each full box of nails weighs 250 g. The boxes are delivered in crates which are cubes of side 0.4 m. An empty crate weighs 20 kg. How much, in kg, would a crate full of these boxes of nails weigh? kg [4] Turn over
4 (a) Solve this inequality. 6 3x 2 10 (a) [2] (b) Represent your solution to part (a) on this number line. 2 1 0 1 2 3 4 5 6 7 8 [1]
5 Petra is designing a small mat to put a glass on. She decides to make the mat a regular hexagon. All the corners should lie on the circle, centre O. One of the corners should be at point A. Construct the hexagon. 7 A O [3] Turn over
6 Sam bought an electronic game on Monday 11th October. The game gives him word and number puzzles to test how well his brain works. He can practise the puzzles to try to improve. The game gives him a Brain Age to show how well he is doing. The Brain Age can range from 65, which is very poor, to 20, which is best. The game uses a time series graph to show Sam s Brain Age. 8 60 50 Brain Age 40 30 20 Mon 11 Oct Mon 18 Oct Mon 25 Oct Mon 1 Nov Mon 8 Nov (a) Complete the time series graph with this information. Date Sam s Brain Age Fri 5 Nov 34 Sat 6 Nov 34 Sun 7 Nov 33 Mon 8 Nov 31 Tues 9 Nov 30 Wed 10 Nov 30 Thur 11 Nov 28 [2]
(b) One day Sam discovers a method to get much better scores. On what date did Sam discover this method? 9 (b) [1] (c) Sam realises he does not do as well when he is ill. Sam was ill for two days in October. On which dates was he ill? (c) [1] (d) Sam s father, John, also likes to play the game occasionally. Date John s Brain Age Tues 12 Oct 38 Wed 20 Oct 30 Sat 23 Oct 35 Mon 1 Nov 28 Thur 11 Nov 29 (i) On the grid, draw the time series graph for John s Brain Age. [1] (ii) Sam thinks he will soon be able to get a better Brain Age than his father all the time. Is Sam correct? Explain your answer. [2] Turn over
7 (a) The sketches of three different straight line graphs are shown below. Write the correct equation under each sketch. Choose from this list. 10 y = 1 2 x + 5 y = 3x + 5 y = x 2 + 5 y = x 5 y = 3x 5 y y y O x O x O x [3] (b) A line, L, is perpendicular to the line y = 2x + 6. L goes through the point (0, 3). Find the equation of the line L. (b) [2]
8* This scatter graph shows the time taken to run 100 metres plotted against age for a group of 18 people. 11 Time taken to run 100 m Age Lizzie says that, for these people, there is no correlation between age and time taken to run 100m. Parand says that, for these people, there is a relationship between age and time taken to run 100 m. Is Lizzie correct? Is Parand correct? Explain your conclusions clearly. [4] Turn over
9 The Park and Ride is a bus service to take people into the city centre. Adults pay 1.60 for a ticket and children pay 20 pence. On one journey there are 55 passengers and the driver collects 67. Let a be the number of adults on the bus and let c be the number of children on the bus. (a) Show that 8a + c = 335. 12 [2] (b) The fact that there are 55 passengers means that a + c = 55. Solve this equation simultaneously with the one from part (a) to find how many children are on the bus. (b) [3]
13 10 The three-toed sloth is a very slow-moving animal. In 2 3 4 33 hours it can only travel 80 of a mile. Use the formula speed = distance time to calculate its average speed in miles per hour. Give your answer as a fraction in its simplest form. mph [3] Turn over
11 A, B, C and D are points on a circle. 14 A 94 B Not to scale 8 cm p C D (a) Work out angle p. Give a reason for your answer. p = because [2] (b)* Is the diameter of the circle less than 8 cm, more than 8 cm or equal to 8 cm? Justify your answer. [3]
15 12 Write the following in the form a 3, where a is an integer. (a) 6 3 (a) [2] (b) 24 2 (b) [2] TURN OVER FOR QUESTION 13
13 (a) On the grid, draw the line 3x + 4y = 12. 16 y 5 4 3 2 1 5 4 3 2 1 0 1 2 3 4 5 6 x 1 2 3 4 5 [2] (b) On the grid, indicate clearly the region R which satisfies all the following inequalities. 3x + 4y < 12 x > 1 y > 0 [2] (c) Write down the integer values of x and y that satisfy all three inequalities. (c) x = y = [1] Copyright Information OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series. If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity. For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE. OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.